CH301&Unit&1GAS&LAWS&REVIEW:&MODELING&GASES,&GAS&LAW&STOICHIOMETRY

MATERIAL&COVERED:&LE01<05,&HW01&Q17<42,&HW02&Q1<3

Goals&for&Today• Introduction*to*gases

• Define*and*describe*gases*qualitatively

• Modeling*Gases

• Discuss*the*eponymous*gas*laws

• Combine*the*gas*laws*into*the*ideal*gas*law

• Extend*the*ideal*gas*law*to*quantify*density

• Gas*Law*Stoichiometry

• Add*one*layer*of*complexity*to*stoichiometry*problems

• Maybe:*Introduction*to*Kinetic*Molecular*Theory

• Describe*the*assumptions*of*KMT

• Introduce*the*relationships*between*kinetic*energy,*temperature

• Introduce*the*relationships*between*velocity*and*mass*of*a*gas

Introduction&to&Gases• As*an*introduction*to*gases,*we*pretend*that*all*gases*are*

“ideal*gases.”

• This*comes*with*a*few*assumptions:

• A*gas*consists*of*a*bunch*of*molecules*that*obey*Newtonian*

physics

• Gas*molecules*are*tiny*spheres*and*they*all*have*the*same*

volume*– however,*this*volume*is*so*small*we*consider*it*

negligible.*Later&on,&we&will&explain&that&this&means&there&are&no&repulsive&forces&present.&

• No*forces*act*upon*these*gas*molecules*except*for*instantaneous,*

perfectly*elastic*collisions*– in&particular,&gas&molecules&do&not&attract&each&other&

Yes,*we*will*refute*these*assumptions*later.*

Modeling&Gases• We*describe*ideal*gases*using*state&functions• State*functions:*a*quantity*or*description*that*explains*the*current*state*of*a*chemical*system

• Another*way*to*describe*them*is*that*they*explain*the*final*and*initial,*but*not*the*process*in*

between

• The*state*functions*we*use*to*describe*gases*are:

1. Pressure*(P):*number*of*collisions between*the*gas*and*the*walls*of*the*container

2. Volume*(V):*the*volume*of*the*container&

3. Temperature*(T):*Kelvin

4. Number*of*moles*(n):*the*quantity of*gas*present

• For*now,*we*can*use*a*few*very*important*relationships*to*model*gases.

Modeling&Gases:&Common&LawsCharles&Law◦ The*volume*and*temperature*of*a*gas*are*directly*proportional

◦ As*temperature*increases,*volume*increases

◦ V/T*=*k◦ V1/T1 =*V2/T2

Boyle’s&Law◦ The*pressure*and*volume*of*a*gas*are*inversely*proportional

◦ As*volume*decreases,*pressure*increases

◦ PV*=*k◦ P1V1 =*P2V2

Avogadro’s&Law◦ The*volume*and*number*of*moles*of*a*gas*are*directly*proportional

◦ V/n*=*k◦ V1/n1 =*V2/n2

• Amonton’s Law*relates*

Pressure*and*

Temperature*in*the*same*

way*as*Charles*Law*(no*

one*cares*about*it*for*

some*reason)

• The*“Bike*Pump”*Law*

relates*Pressure*and*

number*of*moles*in*a*

direct*proportionality*

(pump*in*more*moles*of*

gas,*the*pressure*goes*up)

Exam<Style&QuestionsIf*you*have*a*gas*in*a*closed,*flexible*container*(like*a*balloon,*for*example)*with*a*volume*of*10L*

and*a*pressure*of*0.5atm.*What*volume*container*is*necessary*to*create*a*system*with*a*pressure*

of*1atm*with*the*same*amount*of*gas?

Let’s*go*back*to*our*initial*container:*volume*=*10L*and*pressure*=0.5atm.*What*is*the*volume*of*

your*container*when*you*heat*it*from*25*degrees*Celsius*to*50*degrees*Celsius*at*constant*

pressure?

Hint:*for*the*second*question,*ask*yourself*first*if*it*as*simple*as*doubling?

Exam<Style&QuestionsIf*you*have*a*gas*in*a*closed,*flexible*container*(like*a*balloon,*for*example)*with*a*volume*of*10L*

and*a*pressure*of*0.5atm.*What*volume*container*is*necessary*to*create*a*system*with*a*pressure*

of*1atm*with*the*same*amount*of*gas?*5L

Let’s*go*back*to*our*initial*container:*volume*=*10L*and*pressure*=0.5atm.*What*is*the*volume*of*

your*container*when*you*heat*it*from*25*degrees*Celsius*to*50*degrees*Celsius*at*constant*

pressure?*10.84&L

Hint:*for*the*second*question,*ask*yourself*first*if*it*as*simple*as*doubling? Very&small&change

All&Eponymous&Gas&Laws&Pretty*much*everything*on*the*exam*can*be*solved*using*the*ideal*gas*law,*but*don’t*forget*the*individual*relationships*that*make*it*possible.

• Boyle’s&Law:*Pressure*and*volume*have*an*inverse*relationship*

! ∝1$

• Charles’&Law:*Volume*and*temperature*have*a*direct*relationship

V ∝ &

• Avogadro’s&Law:*Volume*and*number*of*moles*have*a*direct*relationship

V ∝ '

• Bike&Pump&Law:*Pressure*and*number*of*moles*have*a*direct*relationship

P ∝ '

• Amonton’s Law:*Pressure*and*temperature*have*a*direct*relationship

P ∝ &

• HardItoIdoIthis&Law:*number*of*moles*and*temperature*have*an*inverse*relationship

n ∝1&

• Or*just*remember*that*given*

PV=nRT:

• State*functions*on*the*same*

side*have*an*inverserelationship

• State*functions*on*opposite*

sides*have*a*directrelationship

Modeling&Gases:&The&Ideal&Gas&Law• The*relationship*between*these*state*functions*is*presented*in*the*following*equation:

PV*=*nRT

• How*we*use*it:*we*will*use*this*formula*when*we*change*one*state*function*and*keep*all*

other*state*functions*except*one*constant.

• Examples:

• If*you*double&pressure*and*keep*the*same*number*of*moles*and*temperature,*the*volume*will*half.

• If*you*double the*temperature*and*maintain*the*same*number*of*moles*and*pressure,*the*volume*will*double.

• What*about*R?*R*will*never*change*value*unless&you&change&the&units because*it*is*a*constant.*Constants*in*the*natural*sciences*are*used*to*relate*state*functions*with*different*

units.****Make*sure*you*use*the*correct R*value***• Note:*R*is*NOT*a*state*function

The&Universal&Gas&Constant&< RPV*=*nRT

• The&reason&why&this&relationship&works&as&an&equality&is&because&of&the&universal&gas&constant,&R

• The*role*of*R*is*to*cancel*your*units.*If&R does&not&match&the&units&of&pressure,&volume,&moles,&and&temperature,&you&will&end&up&with&the&wrong&value.

• The*units*of*R*stem*from*the*following*relationship:

!$'&

= +,

• For*this*exam,*the*Rdvalue*you*choose*will*be*based*on*your*unit*of*pressure in*the*question

(./0)(2)(034)(5)

= 0.08206+2 ; +./0 ; +034<= ; 5<=+(/3>>)(2)(034)(5)

= 62. 364+2+ ; /3>>+ ; 034<=; 5<=+

Quick&QuestionSTP*is*short*for*“Standard*temperature*and*pressure.”*For*gases*this*is*defined*as*0*degrees*

Celsius*and*1atm*pressure.*Knowing*this,*what*is*the*volume*of*1*mole*gas*at*STP?

R*=*0.08206*L*atm/mol K

R*=*8.314*J/mol K

R*=*62.364*L*torr/mol K

Note:&The&value&you&get&for&this&answer&is&definitely&worth&memorizing&for&the&exam.

The&Ideal&Gas&Law&and&DensityA = BC;D

E;For MW = I+;+E;F

D• You*can*solve*for*the*mass*density*of*a*gas*using*the*molecular*weight*(or*vice*versa)*with*a*

simple*modification*of*the*ideal*gas*law.*

• What*is*density?*

• Number*density*= JK

• Mass*density*(or*just*density)*= LK= A

• Two*takedaway*conceptual*points:

• All&other&conditions&being&equal&in&the&ideal&gas&law&equation&(P,&V,&&&T),&all&ideal&gases&have&the&same&number&density;&number*density*depends*on*P,*V,*&*T*but*NOT*molecular*weight

• All&other&conditions&being&equal&in&the&ideal&gas&law&equation&(P,&V,&&&T),&a&heavier&gas&will&have&a&greater&mass&density;&mass*density*depends*on*the*molecular*weight*of*the*gas

McCordian QuestionYou*have*2.39g*ideal*gas*that*occupies*3L*at*740*torr and*300K.*Which*ideal*gas*is*it?

R*=*0.08206*L*atm/mol K

R*=*8.314*J/mol K

R*=*62.364*L*torr/mol K

a. Helium (4.00&g/mol),&

b. Neon (20.2&g/mol),&

c. Argon (39.95&g/mol),&

d. Krypton (83.8&g/mol),&

e. Xenon (131.3&g/mol)

McCordian QuestionYou*have*2.39g*ideal*gas*that*occupies*3L*at*740*torr and*300K.*Which*ideal*gas*is*it?

R*=*0.08206*L*atm/mol K

R*=*8.314*J/mol K

R*=*62.364*L*torr/mol K

a. Helium (4.00&g/mol),&

b. Neon&(20.2&g/mol),&

c. Argon (39.95&g/mol),&

d. Krypton (83.8&g/mol),&

e. Xenon (131.3&g/mol)

Remember&from&last&week…We*have*covered*the*important*fundamentals*of*stoichiometry.*However,*when*studying*you*

should*always*think:*how&can&we&make&these&questions&more&fun&(a.k.a.*harder)?*Some*

examples*include:*

• Convert&your&number&of&moles&into&mass&or&weight• Use*dimensional*analysis*to*convert*from*moles*to*grams*to*pounds,*etc.

• Dr.*B’s*class:*know*how*to*do*this*by*tomorrow!

• Account&for&an&experimental&percent&yield• Simply*multiply*your*final*answer*by*the*percent*yield

• For*example:*in*the*last*problem*our*answer*was*2.50*moles*of*iron*(III)*oxide.*This*represents*a*

100%*theoretical&yield.*If*the*actual*percent*yield*is*50%,*your*experimental&yield is*1.25*moles*

(2.50*x*0.50).*

• Add&a&gas&law&problem&at&the&end&(we&will&cover&this&later&in&Unit&1)&• For*example,*use*the*total*volume*of*gases*to*solve*for*the*total*pressure

Experimental YieldTheoretical Yield

⋅100%= Percent Yield

Maximum&Difficulty&Stoichiometry&Problem!!!Consider*the*combustion*of*methanol*at*STP.

2CH3OH(g)*+**3O2*(g)*→*2CO2(g)*+ 4H2O(l)

If*13L*of*methanol*reacts*with*8L*oxygen,*how*many*moles*of*gas*are*present*in*the*final*reaction*

mixture?

Kinetic&Molecular&Theory

Kinetic&Molecular&Theory

1. Gases*are*constantly*moving*in*random*directions

2. The*distance*between*particles*is*large*compared*to*the*particle*size

◦ True*ideal*gases*have*relatively*no&volume

3. All*particles*have*perfectly*elastic*collisions

◦ There*is*no*energy*loss*in*the*system*to*collisions;*energy*cannot*be*created*or*destroyed*based*on*Newtonian*Physics

4. No*other*forces*act*upon*ideal*gases

◦ There*are*no*attractive*or*repulsive*forces*that*act*upon*ideal*gas*particles

Main&conclusions:*the*ideal*gas*law*works*because*when*these*pillars*of*KMT*hold*true*in*a*system.*

The*ideal*gas*law*is*modeled*best*at*High&Temperature&and*Low&Pressure

The*ideal*gas*law*fails*us*when*these*

two*assumptions*do*not*hold*true.*We*

will*learn*about*this*later*this*week

Kinetic&Molecular&Theory&explains&the&“energetic”&component&of&gases,&including&kinetic&energy,&velocity,&and&the&relationship&between&kinetic&energy&and&temperature

KMT:&Conceptual&Points1. Kinetic*energy*depends*ONLY*on*temperature

MN+ = +32,&

2. When*you*have*different*gases*at*a*given*temperature:

◦ The*heavy*gases*move*slower*on*average

◦ The&lighter&gases&move&faster&on&average◦ All&gases&have&the&same&kinetic&energy

3. When*you*have*the*same*gas*at*different*temperatures:

◦ The*samples*have*different*kinetic*energies*because*the*temperatures*is*different*and*kinetic&energy&depends&on&temperature

◦ The&hotter&gas&sample&moves&faster&on&average◦ The*colder*gas*sample*moves*slower*on*average

4. Gas*velocity*is*given*as*a*stastistical average*of*velocities,*vrms

◦ Gases*move*at*a*distribution*of*speeds,*although*the&average&kinetic&energy&of&the&sample&depends&only&on&temperature

Summary:• Ideal&gases&are&pretty&easy&if&you&use&the&ideal&gas&law&properly.• Students*who*get*these*problems*wrong*usually*do*one*of*two*things:

• Their*R*value*is*wrong

• They*do*not*convert*from*Celsius*to*Kelvin

• Stoichiometry&is&important&for&gases,&so&learn&it&• Remember*to*differentiate*between*questions*asking*for*the*quantity*of*product*and*the*quantity*of*

total*species*in*the*final*system

• The&average&kinetic&energy&of&a&system&is&only&dependent&on&the&temperature

• Coming*up:

• The*equations*of*KMT

• Mixtures*of*gases:*partial*pressure*and*concentrations

• Deviating*from*ideal*gases:*understanding*that*gas*molecules*have*volume*and*there*are*very*small*

but*nondnegligible*interactions*between*them

• Exam!

Kinetic&Molecular&Theory:&Relationships• Kinetic*Molecules*Theory*gives*us*three*key*relationships*that*you*should*

know*as*equations*and*by*definition*(in*words)

1. Kinetic*Energy*vs.*Temperature

MN+ = +OP,&! Energy&per&mole&(J/mol)

◦ Kinetic&energy&is&dependent&solely&on&the&temperature&of&a&gaseous&system&(direct&relationship)

◦ R*=*8.314*J*/*mol K

MN+ = +OPN& ! Energy&per&molecule&(J)

◦ N+ = EQR+

2. Mass*vs.*Velocity

3. Temperature*vs.*Velocity

Remember*that*in*

physics*we*

describe*kinetic*

energy*with*the*

equation:

120SP

KMT:&Mass&vs.&Velocity;&Velocity&vs.&Temperature1. Kinetic*Energy*vs.*Temperature

Based*on*the*equation:

$TLU = +3,&V

�

We*can*determine*that*velocity*is*proportional*to*the*square&root&of&temperature and*the*inverse&square&root&of*mass.

1. Mass&vs.&Velocity&(Vrms)◦ Velocity*is*proportional*to*the*inverse*square*root*of*mass.

◦ When*temperature*is*constant,*lighter*particles*move*faster

2. Velocity&(Vrms)&vs.&Temperature&◦ Velocity*is*proportional*to*the*square*of*temperature

◦ When*dealing*with*the*same*species*gas,*particles*move*faster*at*higher*temperatures

Pay*very*close*

attention*to*how*

the*1*and*2*match*

up*in*these*

relationships

XYXZ= BZ

BY

�

XYXZ= FY

FZ

�

Molecular*Weight*in*Kg

R*=*8.314*J/mol K

Practice&ProblemWhat*is*the*ratio*of*the*effusion*rates*of*SO2 to*Cl2?

If*the*velocity*of*Cl2 is*500m/s,*what*is*the*temperature?

X[\ZX]^Z

=B]^ZB[\Z

� The*position*of*these*is*

important*because*it*is*asking*

you*for*the*ratio*of*SO2*:*Cl2

$_`Z = +3,&V

�

KMT:&Mass&vs.&Velocity;&Velocity&vs.&Temperature

1. Mass&vs.&Velocity&(Vrms)◦ We*can*see*that*the*heavier*gases move*

slower and*the*lighter*gases*move*faster

◦ The*faster the*gas,*the*wider the*

distribution

2. Velocity&(Vrms)&vs.&Temperature&◦ If*you*were*working*with*the*same*gas,*

a*similar*graph*could*be*created*by*

modifying*temperature*instead.*

◦ In*this*case,*higher*temperatures*of*the*

same*gas*result*in*faster*speeds.

• Some*key*features*of*this*graph*include:

• Each*curve*looks*like*a*unimodal*distribution*with*a*“tail”*that*approaches*the*limit*infinite*velocity*(0*probability*density)*

• Molecules*are*traveling*at*a*variety*of*speeds*but*there*is*a*clear*average

• The*actual*Vrms is*slightly*to*the*right*of*the*peak

Maxwell<Boltzmann&Distribution• Given*a*Maxwell*distribution,*you*should*know:

• Find*the*approximate*Vrms

• Be*able*to*label*which&gas&is&which&(or*which*temperature*is*

which)

• Understand*the*relationships between*mass,*velocity,*and*

temperature*

• Understand*how*these*relationships*impact*the*shape&of*the*curve